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If int(0)^(x) f ( t) dt = x + int(x)^(1)...

If `int_(0)^(x) f ( t) dt = x + int_(x)^(1) tf (t) dt `, then the value of f(1) is

A

`(1)/(2)`

B

2

C

1

D

`(3)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
`(1)/(2)`
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SURA PUBLICATION-APPLICATION OF INTEGRATION -EXERCISE 9.10
  1. The value of int(0)^((2)/( 3)) (dx)/( sqrt(4-9x^(2)))is

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  2. The value of int(-1)^(2) |x| dx

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  3. For any value of n in Z , int(0)^(pi) e^(cos^(2)x) cos^(3) [( 2n +1) x...

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  4. The value of int(-(pi)/(2)) ^((pi)/(2)) sin^(2) x cos x dx is

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  5. The value of int(-4)^(4) [ tan^(-1)((x^(2))/( x^(4)+1)) +tan^(-1) ((x...

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  6. The value of int(-(pi)/(4))^((pi)/( 4)) ((2x^(7) - 3x^(5) + 7 x^(3) -...

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  7. If f(x) = int(0)^(x) t cos t dt, then (df)/(dx)

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  8. The area between y^(2) = 4x and its latus rectum is

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  9. The value of int(0)^(1) x ( 1-x ) ^(99) dx is

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  10. The value of int(0)^(pi)dx/(1+5^(cosx)) is :

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  11. The value of (r(n+2))/(r(n))=90 then n is

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  12. The value of int(0)^((pi)/(6)) cos ^(3) 3x dx

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  13. The value of int(0)^(pi) sin^(4) x dx is

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  14. The value of int(0)^(oo) e^(-3x) x^(2) dx is

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  15. If int(0)^(a) = ( 1)/( 4+x^(2))dx = ( pi)/( 8) then a is

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  16. The volume of solid of revolution of the region bounded by y^(2)= x( a...

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  17. If f(x) = int(1)^(x) ( e^(sinx )) /( u) du, x gt 1 and int(1)^(3) ( ...

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  18. The value of int(0)^(1) (sin^(-1) x ) ^(2) dx is

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  19. The value of int(0)^(a) ( sqrt(a^(2) -x^(2))) dx is

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  20. If int(0)^(x) f ( t) dt = x + int(x)^(1) tf (t) dt , then the value of...

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